The Information Content of Implied Probabilities to Detect Structural Change

This paper proposes Pearson-type statistics based on implies probabilities to detect structural change. The class of generalized empirical likelihood estimators (see Smith (1997)) assigns a set of probabilities to each observation such that moment conditions are satisfied. These restricted probabilities are called implied probabilities. Implied probabilities may also be constructed for the standard GMM (see Back and Brown (1993)). The proposed test statistics for structural change are based on the information content in these implied probabilities. We consider cases of structural change with unknown breakpoint which can occur in the parameters of interest or in the overidentifying restrictions used to estimate these parameters. The test statistics considered here have good size and power properties.Generalized empirical likelihood, generalized method of moments, parameter instability, structural change

Path Functors in Cat

We build an endofunctor in the category of small categories along with the necessary structure on it to turn it into a path object suitable for homotopy theory and modelling identity types in Martin-L\ ̈of type theory. We construct the free Grothendieck bifibration over a base category generated by an arbitrary functor to that category

Modeling Martin Löf Type Theory in Categories

International audienceWe present a model of Martin-Lof type theory that includes both dependent products and the identity type. It is based on the category of small categories, with cloven Grothendieck bifibrations used to model dependent types. The identity type is modeled by a path functor that seems to have independent interest from the point of view of homotopy theory. We briefly describe this model's strengths and limitations

From Proof Nets to the Free *-Autonomous Category

In the first part of this paper we present a theory of proof nets for full multiplicative linear logic, including the two units. It naturally extends the well-known theory of unit-free multiplicative proof nets. A linking is no longer a set of axiom links but a tree in which the axiom links are subtrees. These trees will be identified according to an equivalence relation based on a simple form of graph rewriting. We show the standard results of sequentialization and strong normalization of cut elimination. In the second part of the paper we show that the identifications enforced on proofs are such that the class of two-conclusion proof nets defines the free *-autonomous category.Comment: LaTeX, 44 pages, final version for LMCS; v2: updated bibliograph

L'Université Médicale Virtuelle Francophone (UMVF)

International audienceCe chapitre fait partie d’une publication collective de l’ERTe (Équipe de Recherche Technologique éducation) "Modèles économiques et enjeux organisationnels des campus numériques". L'ensemble de la publication est consultable sur le site de l'IFRÉSI à Lille à http://www.ifresi.univ-lille1.fr/SITE/2_Recherche/22_Programmes/ERTe/ERTe.htm ou sur un site dédié de la MSH Paris Nord à http://erte.mshparisnord.org

Proof Nets for Intuitionistic Linear Logic: Essential Nets

We present a class of proof nets that are specially designed for Intuitionistic Linear Logic, for which we give a correctness criterion, as well as a cut-elimination procedure. The proof of sequentialization uses a special kind of oriented paths

Homotopy in Cat via Paths and the Fundamental Groupoid of a Category

We construct an endofunctor of paths in the category of small category and show how to construct the standard homotopy invariants from it. We give a novel proof that the fundamental groupoid of a category is its associated universal groupoid

On the Algebra of Structural Contexts

Article dans revue scientifique avec comité de lecture.We discuss a general way of defining contexts in linear logic, based on the observation that linear universal algebra can be symmetrized by assigning an additional variable to represent the output of a term. We give two approaches to this, a syntactical one based on a new, reversible notion of term, and an algebraic one based on a simple generalization of typed operads. We relate these to each other and to known examples of logical systems, and show new examples, in particular discussing the relationship between intuitionistic and classical systems. We then present a general framework for extracting deductive system from a given theory of contexts, and prove that all these systems have cut-elimination by the means of a generic argument

Constructing orders by means of inductive definitions

Rapport interne.We present a class of algebraic theories that are enriched over a novel symmetrical monoidal closed structure on the category of graphs, whose free models are posets that are equipped with an induction principle, which is easily formalized in type theory. We give examples